Given $ m \angle CBD = 5x - 62$, and $ m \angle ABC = 9x + 18$, find $m\angle CBD$. $B$ $A$ $D$ $C$
Answer: From the diagram, we see that together ${\angle ABC}$ and ${\angle CBD}$ form ${\angle ABD}$ , so $ {m\angle ABC} + {m\angle CBD} = {m\angle ABD}$ Since $\angle ABD$ is a straight angle, we know ${m\angle ABD = 180}$ Substitute in the expressions that were given for each measure: $ {9x + 18} + {5x - 62} = {180}$ Combine like terms: $ 14x - 44 = 180$ Add $44$ to both sides: $ 14x = 224$ Divide both sides by $14$ to find $x$ $ x = 16$ Substitute $16$ for $x$ in the expression that was given for $m\angle CBD$ $ m\angle CBD = 5({16}) - 62$ Simplify: $ {m\angle CBD = 80 - 62}$ So ${m\angle CBD = 18}$.